Drawing atomic structure requires only a simple understanding of the components of atomic structure. If you understand how protons and electrons relate to one another, as well as how neutrons aid in comprising atomic mass, the rest is cake.
Drawing Atomic Structure
Draw a circle on the page. For the purposes of this article, we'll use carbon as an example. The process is the same for whatever you're drawing, however. Write a letter "C" in the middle of the circle as an annotation that you're dealing with carbon.
Determine how many protons and electrons you'll need to draw. The amount of electrons in an atom is tied to the amount of protons. However many protons you have, that's how many electrons you'll need. To determine the number of protons, you just look at the atomic number. The atomic number for carbon is 6, so you'll need 6 protons, and in turn 6 electrons.
Draw your electron rings. The circle with the "C" is a representative nucleus, so now you'll need to indicate the electron orbitals. The number of rings you need is to tied to the number of electrons you have. Carbon has 6 electrons. Since each ring has a maximum number of electrons that can be pictured, you'll have to do some math. The first ring can have a maximum of 2 electrons, the second ring a maximum of 8, the third ring a maximum of 18, etc. Carbon has 6 electrons, so you'll need to draw two concentric rings.
Draw your electrons. You can do this a couple different ways. Some people just draw circles on the rings and fill them in. In this case, you would draw 2 on the first ring and 4 on the second ring. You can also indicate electrons by drawing X's. The best way to draw electrons is to draw them as circles with minus signs inside. This indicates not only that they are electrons, but helps remind the viewer that electrons contain a negative charge.
Draw your protons and neutrons. Erase the "C" in the center circle, and draw in your protons. Since protons are the same as the amount of electrons, you just draw 6 protons. To indicate they are protons, draw them as circles with plus signs contained inside. Neutrons are simply equal to the atomic mass minus the number of protons. Again, you'll need to do some quick math. The atomic mass of carbon is 12, and you have 6 protons. That means you need to draw 6 neutrons in your nucleus. Do not give them an indication of charge, as neutrons are of neutral charge.
Label your diagram if you want. It should be clear from your drawing which element is being indicated, but it can never hurt to clarify.
TL;DR (Too Long; Didn't Read)
Use pencil first, in case you make a mistake.
Do your calculations before you make your drawing. It's easier to draw the diagram once you know exactly how many of everything you have to have down.
Double-check your math, especially on the elements with larger atomic numbers. One misplaced or forgotten, the electron and your entire diagram is worthless.